Find the intervals on which f(x) is increasing, the intervals on which f(x) is decreasing, and thelocal extrema.fx)= -4x-32x-27Select the correct choice below and, if necessary, fill in the answer box to complete yourchoice.OA. The function is increasing on(Type your answer in interval notation. Type integers or simplified fractions. Use a comma to separate answers as needed.)O B. The function is never increasingSelect the correct choice below and, if necessary, fill in the answer box to complete your choice.eadlO A. The function is decreasing onw (O(Type your answer in interval notation. Type integers or simplified fractions. Use a comma to separate answers as needed.)O B. The function is never decreasing.Select the corect choice below and, if necessary, fill in the answer boxes to complete your choice(Type integers or simplified fractions.)O A. The function has a local minimum f(|and no local maximum.OB. The function has a local maximum fand a local minimum f)=amOC. The function has a local maximumfand no local minimum.O D. The function has no local extrema- 6n InformGradesWithdray$?Click to select and enter your answer(s).dia LibrarType here to search

Question
Asked Nov 6, 2019
Find the intervals on which f(x) is increasing, the intervals on which f(x) is decreasing, and the
local extrema.
fx)= -4x-32x-27
Select the correct choice below and, if necessary, fill in the answer box to complete your
choice.
OA. The function is increasing on
(Type your answer in interval notation. Type integers or simplified fractions. Use a comma to separate answers as needed.)
O B. The function is never increasing
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
eadl
O A. The function is decreasing on
w (O
(Type your answer in interval notation. Type integers or simplified fractions. Use a comma to separate answers as needed.)
O B. The function is never decreasing.
Select the corect choice below and, if necessary, fill in the answer boxes to complete your choice
(Type integers or simplified fractions.)
O A. The function has a local minimum f(|
and no local maximum.
OB. The function has a local maximum f
and a local minimum f)=
am
OC. The function has a local maximumf
and no local minimum.
O D. The function has no local extrema
- 6
n Inform
Grades
Withdray
$?
Click to select and enter your answer(s).
dia Librar
Type here to search
help_outline

Image Transcriptionclose

Find the intervals on which f(x) is increasing, the intervals on which f(x) is decreasing, and the local extrema. fx)= -4x-32x-27 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. OA. The function is increasing on (Type your answer in interval notation. Type integers or simplified fractions. Use a comma to separate answers as needed.) O B. The function is never increasing Select the correct choice below and, if necessary, fill in the answer box to complete your choice. eadl O A. The function is decreasing on w (O (Type your answer in interval notation. Type integers or simplified fractions. Use a comma to separate answers as needed.) O B. The function is never decreasing. Select the corect choice below and, if necessary, fill in the answer boxes to complete your choice (Type integers or simplified fractions.) O A. The function has a local minimum f(| and no local maximum. OB. The function has a local maximum f and a local minimum f)= am OC. The function has a local maximumf and no local minimum. O D. The function has no local extrema - 6 n Inform Grades Withdray $? Click to select and enter your answer(s). dia Librar Type here to search

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check_circleExpert Solution
Step 1

Given function is,

f(x)=-4x2-32x- 27
Find the derivative of the functionf (x).
f'(x)(-4x2-32x-27)
— — 8х — 32
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f(x)=-4x2-32x- 27 Find the derivative of the functionf (x). f'(x)(-4x2-32x-27) — — 8х — 32

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Step 2

Obtain the critic...

Solvef'(r)0
-8x-32 0
-8x 32
x =-4
The intervals of the function
(4)u(-4,)
Check the sign of the function
Decision Sign
Interval
Functional value
,-4)f(5) = -8(-5)-32Increasing
= 40 32
8>0
(-4, )
f'(-3)-8(-3)-32 Decreasing
- 24-32
=-8<0
In the interval, -o,-4), the function is increasing and the interval (-4,o) the function
decreasing
help_outline

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Solvef'(r)0 -8x-32 0 -8x 32 x =-4 The intervals of the function (4)u(-4,) Check the sign of the function Decision Sign Interval Functional value ,-4)f(5) = -8(-5)-32Increasing = 40 32 8>0 (-4, ) f'(-3)-8(-3)-32 Decreasing - 24-32 =-8<0 In the interval, -o,-4), the function is increasing and the interval (-4,o) the function decreasing

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